Ocean sequestration of carbon dioxide: modeling the deep ocean release of a dense emulsion of liquid Co2-in-water stabilized by pulverized limestone particles

The release into the deep ocean of an emulsion of liquid carbon dioxide-in-seawater stabilized by fine particles of pulverized limestone (CaCO3) is modeled. The emulsion is denser than seawater, hence, it will sink deeper from the injection point, increasing the sequestration period. Also, the presence of CaCO3 will partially buffer the carbonic acid that results when the emulsion eventually disintegrates. The distance that the plume sinks depends on the density stratification of the ocean, the amount of the released emulsion, and the entrainment factor. When released into the open ocean, a plume containing the CO2 output of a 1000 MW(el) coal-fired power plant will typically sink hundreds of meters below the injection point. When released from a pipe into a valley on the continental shelf, the plume will sink about twice as far because of the limited entrainment of ambient seawater when the plume flows along the valley. A practical system is described involving a static mixer for the in situ creation of the CO2/seawater/pulverized limestone emulsion. The creation of the emulsion requires significant amounts of pulverized limestone, on the order of 0.5 tons per ton of liquid CO2. That increases the cost of ocean sequestration by about $13/ ton of CO2 sequestered. However, the additional cost may be compensated by the savings in transportation costs to greater depth, and because the release of an emulsion will not acidify the seawater around the release point.

Limestone-particle-stabilized macroemulsion of liquid and supercritical carbon dioxide in water for ocean sequestration

When liquid or supercritical CO2 is mixed with an aqueous slurry of finely pulverized (1-20 microm) limestone (CaCO3) in a high-pressure reactor, a macroemulsion is formed consisting of droplets of CO2 coated with a sheath of CaCO3 particles dispersed in water. The coated droplets are called globules. Depending on the globule diameter and the CaCO3 sheath thickness, the globules sink to the bottom of the water column, are neutrally buoyant, or float on top of the water. The CaCO3 particles are lodged at the CO2/ H2O interface, preventing the coalescence of the CO2 droplets, and thus stabilizing the CO2-in-water emulsion. We describe the expected behavior of a CO2/H2O/CaCO3 emulsion plume released in the deep ocean for sequestration of CO2 in the ocean to ameliorate global warming. Depending on the amount of CO2 injected, the dense plume will descend a few hundred meters while entraining ambient seawater until it acquires neutral buoyancy in the stratified ocean. After equilibration, the globules will rain out from the plume toward the ocean bottom. This mode of CO2 release will prevent acidification of the seawater around the release point, which is a major environmental drawback of ocean sequestration of liquid, unemulsified CO2.

Period doubling of calcium spike firing in a model of a Purkinje cell dendrite

Recordings from cerebellar Purkinje cell dendrites have revealed that in response to sustained current injection, the cell firing pattern can move from tonic firing of Ca(2+) spikes to doublet firing and even to quadruplet firing or more complex firing. These firing patterns are not modified substantially if Na(+) currents are blocked. We show that the experimental results can be viewed as a slow transition of the neuronal dynamics through a period-doubling bifurcation. To further support this conclusion and to understand the underlying mechanism that leads to doublet firing, we develop and study a simple, one-compartment model of Purkinje cell dendrite. The neuron can also exhibit quadruplet and chaotic firing patterns that are similar to the firing patterns that some of the Purkinje cells exhibit experimentally. The effects of parameters such as temperature, applied current, and potassium reversal potential in the model resemble their effects in experiments. The model dynamics involve three time scales. Ca(2+)- dependent K(+) currents, with intermediate time scales, are responsible for the appearance of doublet firing, whereas a very slow hyperpolarizing current transfers the neuron from tonic to doublet firing. We use the fast-slow analysis to separate the effects of the three time scales. Fast-slow analysis of the neuronal dynamics, with the activation variable of the very slow, hyperpolarizing current considered as a parameter, reveals that the transitions occurs via a cascade of period-doubling bifurcations of the fast and intermediate subsystem as this slow variable increases. We carry out another analysis, with the Ca(2+) concentration considered as a parameter, to investigate the conditions for the generation of doublet firing in systems with one effective variable with intermediate time scale, in which the rest state of the fast subsystem is terminated by a saddle-node bifurcation. We find that the scenario of period doubling in these systems can occur only if (1) the time scale of the intermediate variable (here, the decay rate of the calcium concentration) is slow enough in comparison with the interspike interval of the tonic firing at the transition but is not too slow and (2) there is a biostability of the fast subsystem of the spike-generating variables.

Bistability in pulse propagation in networks of excitatory and inhibitory populations

We study the propagation of traveling solitary pulses in one-dimensional networks of excitatory and inhibitory integrate-and-fire neurons. Slow pulses, during which inhibitory cells fire well before neighboring excitatory cells, can propagate along the network at intermediate inhibition levels. At higher levels, they destabilize via a Hopf bifurcation. There is a bistable parameter regime in which both fast and slow pulses can propagate. Lurching pulses with spatiotemporal periodicity can propagate in regimes for which continuous pulses do not exist.

Effects of delay on the type and velocity of travelling pulses in neuronal networks with spatially decaying connectivity

We study a one-dimensional model of integrate-and-fire neurons that are allowed to fire only one spike, and are coupled by excitatory synapses with delay. At small delay values, this model describes a disinhibited cortical slice. At large delay values, the model is a reduction of a model of thalamic networks composed of excitatory and inhibitory neurons, in which the excitatory neurons show the post-inhibitory rebound mechanism. The velocity and stability of propagating continuous pulses are calculated analytically. Two pulses with different velocities exist if the synaptic coupling is larger than a minimal value; the pulse with the lower velocity is always unstable. Above a certain critical value of the constant delay, continuous pulses lose stability via a Hopf bifurcation, and lurching pulses emerge. The parameter regime for which lurching occurs is strongly affected by the synaptic footprint (connectivity) shape. A bistable regime, in which both continuous and lurching pulses can propagate. may occur with square or Gaussian footprint shapes but not with an exponential footprint shape. A perturbation calculation is used in order to calculate the spatial lurching period and the velocity of lurching pulses at large delay values. For strong synaptic coupling, the velocity of the lurching pulse is governed by the tail of the synaptic footprint shape. Moreover, the velocities of continuous and lurching pulses have the same functional dependencies on the strength of the synaptic coupling strength gsyn: they increase logarithmically with gsyn for an exponential footprint shape, they scale like (In gsyn)1/2 for a Gaussian footprint shape, and they are bounded for a square footprint shape or any shape with a finite support. We find analytically how the axonal propagation velocity reduces the velocity of continuous pulses; it does not affect the critical delay. We conclude that the differences in velocity and shape between the front of thalamic spindle waves in vitro and cortical paroxysmal discharges stem from their different effective delays.

The number of synaptic inputs and the synchrony of large, sparse neuronal networks

The prevalence of coherent oscillations in various frequency ranges in the central nervous system raises the question of the mechanisms that synchronize large populations of neurons. We study synchronization in models of large networks of spiking neurons with random sparse connectivity. Synchrony occurs only when the average number of synapses, M, that a cell receives is larger than a critical value, Mc. Below Mc, the system is in an asynchronous state. In the limit of weak coupling, assuming identical neurons, we reduce the model to a system of phase oscillators that are coupled via an effective interaction, gamma. In this framework, we develop an approximate theory for sparse networks of identical neurons to estimate Mc analytically from the Fourier coefficients of gamma. Our approach relies on the assumption that the dynamics of a neuron depend mainly on the number of cells that are presynaptic to it. We apply this theory to compute Mc for a model of inhibitory networks of integrate-and-fire (I&F) neurons as a function of the intrinsic neuronal properties (e.g., the refractory period Tr), the synaptic time constants, and the strength of the external stimulus, Iext. The number Mc is found to be nonmonotonous with the strength of Iext. For Tr = 0, we estimate the minimum value of Mc over all the parameters of the model to be 363.8. Above Mc, the neurons tend to fire in smeared one-cluster states at high firing rates and smeared two-or-more-cluster states at low firing rates. Refractoriness decreases Mc at intermediate and high firing rates. These results are compared to numerical simulations. We show numerically that systems with different sizes, N, behave in the same way provided the connectivity, M, is such that 1/Meff = 1/M - 1/N remains constant when N varies. This allows extrapolating the large N behavior of a network from numerical simulations of networks of relatively small sizes (N = 800 in our case). We find that our theory predicts with remarkable accuracy the value of Mc and the patterns of synchrony above Mc, provided the synaptic coupling is not too large. We also study the strong coupling regime of inhibitory sparse networks. All of our simulations demonstrate that increasing the coupling strength reduces the level of synchrony of the neuronal activity. Above a critical coupling strength, the network activity is asynchronous. We point out a fundamental limitation for the mechanisms of synchrony relying on inhibition alone, if heterogeneities in the intrinsic properties of the neurons and spatial fluctuations in the external input are also taken into account.

Continuous and lurching traveling pulses in neuronal networks with delay and spatially decaying connectivity

Propagation of discharges in cortical and thalamic systems, which is used as a probe for examining network circuitry, is studied by constructing a one-dimensional model of integrate-and-fire neurons that are coupled by excitatory synapses with delay. Each neuron fires only one spike. The velocity and stability of propagating continuous pulses are calculated analytically. Above a certain critical value of the constant delay, these pulses lose stability. Instead, lurching pulses propagate with discontinuous and periodic spatio-temporal characteristics. The parameter regime for which lurching occurs is strongly affected by the footprint (connectivity) shape; bistability may occur with a square footprint shape but not with an exponential footprint shape. For strong synaptic coupling, the velocity of both continuous and lurching pulses increases logarithmically with the synaptic coupling strength g(syn) for an exponential footprint shape, and it is bounded for a step footprint shape. We conclude that the differences in velocity and shape between the front of thalamic spindle waves in vitro and cortical paroxysmal discharges stem from their different effective delay; in thalamic networks, large effective delay between inhibitory neurons arises from their effective interaction via the excitatory cells which display postinhibitory rebound.

Models of neuronal transient synchrony during propagation of activity through neocortical circuitry

Stereotypic paroxysmal discharges that propagate in neocortical tissues after electrical stimulations are used as a probe for studying cortical circuitry. I use modeling to investigate the effects of sparse connectivity, heterogeneity of intrinsic neuronal properties, and synaptic noise on synchronization of evoked propagating neuronal discharges in a network of excitatory, regular spiking neurons with spatially decaying connectivity. The global coherence of the traveling discharge is characterized by the correlation function between spike trains of neurons, averaged over all the pairs of neurons in the system at the same distance. Local coherence of two neurons is characterized by their correlation function averaged over many trials or, for persistent activity, over a long time interval. Spike synchronization between neurons emerges as a result of the transient activity; if activity is persistent, there is no synchrony, and cross-correlation functions are flat. During discharge propagation, system-average cross-correlation between neurons does not depend on their mutual distance except for a time shift. Spike synchronization occurs only when the average number of synapses M a cell receives is large enough. As M increases, there is a cross-over from an asynchronized to a synchronized discharge. Synaptic depression appears to help synchrony; it reduces the M value at the cross-over. The strengths of alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl-D-aspartate (NMDA) conductances affect synchrony only weakly. Spike synchronization is robust even with large levels of heterogeneity. Synaptic noise reduces synchrony, but strong synchrony is observed at a noise level that cannot evoke spontaneous discharges. System-average spike synchronization is determined by the levels of sparseness, heterogeneity, and noise, whereas trial-average spike synchronization is determined only by the noise level. Therefore, I predict that experiments will reveal local, two-cell spike synchrony, but not global synchrony.

Propagating neuronal discharges in neocortical slices: computational and experimental study

We studied the propagation of paroxysmal discharges in disinhibited neocortical slices by developing and analyzing a model of excitatory regular-spiking neocortical cells with spatially decaying synaptic efficacies and by field potential recording in rat slices. Evoked discharges may propagate both in the model and in the experiment. The model discharge propagates as a traveling pulse with constant velocity and shape. The discharge shape is determined by an interplay between the synaptic driving force and the neuron's intrinsic currents, in particular the slow potassium current. In the model, N-methyl-D-aspartate (NMDA) conductance contributes much less to the discharge velocity than amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) conductance. Blocking NMDA receptors experimentally with 2-amino-5-phosphonovaleric acid (APV) has no significant effect on the discharge velocity. In both model and experiments, propagation occurs for AMPA synaptic coupling gAMPA above a certain threshold, at which the velocity is finite (non-zero). The discharge velocity grows linearly with the gAMPA for gAMPA much above the threshold. In the experiments, blocking AMPA receptors gradually by increasing concentrations of 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) in the perfusing solution results in a gradual reduction of the discharge velocity until propagation stops altogether, thus confirming the model prediction. When discharges are terminated in the model by the slow potassium current, a network with the same parameter set may display discharges with several forms, which have different velocities and numbers of spikes; initial conditions select the exhibited pattern. When the discharge is also terminated by strong synaptic depression, there is only one discharge form for a particular parameter set; the velocity grows continuously with increased synaptic conductances. No indication for more than one discharge velocity was observed experimentally. If the AMPA decay rate increases while the maximal excitatory postsynaptic conductance (EPSC) a cell receives is kept fixed, the velocity increases by approximately 20% until it reaches a saturated value. Therefore the discharge velocity is determined mainly by the cells' integration time of input EPSCs. We conclude, on the basis of both the experiments and the model, that the total amount of excitatory conductance a typical cell receives in a control slice exhibiting paroxysmal discharges is only approximately 5 times larger than the excitatory conductance needed for raising the potential of a resting cell above its action potential threshold.

How well can we estimate the information carried in neuronal responses from limited samples?

It is difficult to extract the information carried by neuronal responses about a set of stimuli because limited data samples result in biased estimates. Recently two improved procedures have been developed to calculate information from experimental results: a binning-and-correcting procedure and a neural network procedure. We have used data produced from a model of the spatiotemporal receptive fields of parvocellular and magnocellular lateral geniculate neurons to study the performance of these methods as a function of the number of trials used. Both procedures yield accurate results for one-dimensional neuronal codes. They can also be used to produce a reasonable estimate of the extra information in a three-dimensional code, in this instance, within 0.05-0.1 bit of the asymptotically calculated value--about 10% of the total transmitted information. We believe that this performance is much more accurate than previous procedures.

Propagation of spindle waves in a thalamic slice model

1. We study the propagation and dynamics of spindle waves in thalamic slices by developing and analyzing a model of reciprocally coupled populations of excitatory thalamocortical (TC) neurons and inhibitory thalamic reticular (RE) neurons. 2. Each TC neuron has three intrinsic ionic currents: a low-threshold T-type Ca+2 current (ICa-T), a hyperpolarization-activated cation ("sag") current (Ih) and a leak current. Each RE cell also has three currents: ICa-T, a leak current, and a calcium-activated potassium current (IAHP). Isolated TC cells are at rest, can burst when released or depolarized from a hyperpolarized level, and burst rhythmically under moderate constant hyperpolarizing current. Isolated RE cells are at a hyperpolarized resting membrane potential and can burst when depolarized. 3. TC cells excite RE cells with fast alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) synapses, and RE cells inhibit TC cells with fast gamma-aminobutyric acid-A (GABAA) and slow GABAB synapses and inhibit each other with GABAA synapses only. GABAB postsynaptic conductances operate far from saturation, and the slow inhibitory postsynaptic potentials (IPSPs) increase with the width of the presynaptic burst. The model network is a one-dimensional cellular array with localized coupling. The synaptic coupling strength decays with the distance between the pre- and postsynaptic cells, either exponentially or as a step function. 4. The "intact" network can oscillate with partial synchrony and a population frequency of approximately 10 Hz. RE cells emit bursts almost at every oscillation cycle, whereas TC cells do so almost at every other cycle. Block of GABAB receptors hardly changes the network behavior. Block of GABAA receptors leads the network to a slowed oscillatory state, where the population frequency is approximately 4 Hz and both RE and TC cells fire unusually long bursts at every cycle and in full synchrony. These results are consistent with the experimental observations of von Krosigk, Bal, and McCormick. We obtain such consistency only when the above assumptions regarding the synaptic dynamics, particularly nonsaturating GABAB synapses, are fulfilled. 5. The slice model has a stable rest state with no neural activity. By initially depolarizing a few neurons at one end of the slice while all the other cells are at rest, a recruitment process may be initiated, and a wavefront of oscillatory activity propagates across the slice. Ahead of the wavefront, neurons are quiescent; neurons behind it oscillate. We find that the wave progresses forward in a lurching manner. TC cells that have just become inhibited must be hyperpolarized for a long enough time before they can fire rebound bursts and recruit RE cells. This step limits the wavefront velocity and may involve a substantial part of the cycle when no cells at the front are depolarized. 6. The wavefront velocity increases linearly with the characteristic spatial length of the connectivity (the footprint length). It increases only gradually with the synaptic strength, logarithmically in the case of an exponential connection function and only slightly for a step connection function. It also decreases gradually with a potassium leak conductance that hyperpolarizes RE cells. 7. To reproduce the experimentally measured wavefront velocity of approximately 1 mm/s, together with other in vitro observations, both the RE-to-TC and the TC-to-RE projections in the model should be spatially localized. The sum of the RE-to-TC and the TC-to-RE synaptic footprint lengths should be on the order of 100 microns. (ABSTRACT TRUNCATED AT 250 WORDS)

Emergent spindle oscillations and intermittent burst firing in a thalamic model: specific neuronal mechanisms

The rhythmogenesis of 10-Hz sleep spindles is studied in a large-scale thalamic network model with two cell populations: the excitatory thalamocortical (TC) relay neurons and the inhibitory nucleus reticularis thalami (RE) neurons. Spindle-like bursting oscillations emerge naturally from reciprocal interactions between TC and RE neurons. We find that the network oscillations can be synchronized coherently, even though the RE-TC connections are random and sparse, and even though individual neurons fire rebound bursts intermittently in time. When the fast gamma-aminobutyrate type A synaptic inhibition is blocked, synchronous slow oscillations resembling absence seizures are observed. Near-maximal network synchrony is established with even modest convergence in the RE-to-TC projection (as few as 5-10 RE inputs per TC cell suffice). The hyperpolarization-activated cation current (Ih) is found to provide a cellular basis for the intermittency of rebound bursting that is commonly observed in TC neurons during spindles. Such synchronous oscillations with intermittency can be maintained only with a significant degree of convergence for the TC-to-RE projection.

On temporal codes and the spatiotemporal response of neurons in the lateral geniculate nucleus

1. The present work relates recent experimental studies of the temporal coding of visual stimuli (McClurkin, Optican, Richmond, and Gawne, Science 253: 675, 1991) to the measurements of the spatiotemporal receptive fields of neurons within the lateral geniculate of primate. 2. We analyze both new and previously described magnocellular and parvocellular single units. The spatiotemporal impulse response function of the unit, defined as the time-resolved average firing rate in response to a weak stimulus flashed at a given location and time, is characterized by the singular value decomposition. This analysis allows one to represent the impulse response by a small number, two to three, of spatial and temporal modes. Both magnocellular and parvocellular units are weakly nonseparable, with major and minor modes that account, respectively, for approximately 78 and 22% of the response. The major temporal mode for both types is essentially identical for the first 100 ms. At later times the response of magnocellular units changes sign and decays slowly, whereas the response of parvocellular units decays relatively rapidly. 3. The spatiotemporal impulse response function completely determines the response of a unit to an arbitrary stimulus when linear response theory is valid. Using the measured impulse response, combined with a rectifying neuronal input-output relation, we calculate the responses to a complete set of spatial luminance patterns constructed of "Walsh" functions. Our predicted temporal responses are in qualitative agreement with those reported for parvocellular units (McClurkin, Optican, Richmond, and Gawne, J. Neurophysiol. 66: 794, 1991). Under the additional assumptions of Poisson statistics for the probability of spiking and a plausible background firing rate, we predict the performance of a unit in the Walsh pattern discrimination task as quantified by mutual information. Our prediction is again consistent with the reported results. 4. Last, we consider the issue of temporal coding within linear response. For stimuli presented for fixed time intervals, the singular value decomposition provides a natural relation between the temporal modes of the neuronal response and the spatial pattern of the stimulus. Although it is tempting to interpret each temporal mode as an independent channel that encodes orthogonal features of the stimulus, successively higher order modes are increasingly unreliable and do not significantly increase the discrimination capabilities of the unit.

Synchronization properties of spindle oscillations in a thalamic reticular nucleus model

Pages 1109–1126: D. Golomb, X.-J. Wang, and J. Rinzel. “Synchronization properties of spindle oscillations in a thalamic reticular nucleus model.” The following errors were inadvertently introduced when this article was printed. Page 1125, in the list of references, all the journal titles written as Physiol. Rev. should be Phys. Rev., and all the journal titles written as Physiol. Rev. Lett. should be Phys. Rev. Lett.

Synchronization properties of spindle oscillations in a thalamic reticular nucleus model

1. We address the hypothesis of Steriade and colleagues that the thalamic reticular nucleus (RE) is a pacemaker for thalamocortical spindle oscillations by developing and analyzing a model of a large population of all-to-all coupled inhibitory RE neurons. 2. Each RE neuron has three ionic currents: a low-threshold T-type Ca2+ current (ICa-T), a calcium-activated potassium current (IAHP) and a leakage current (IL). ICa-T underlies a cell's postinhibitory rebound properties, whereas IAHP hyperpolarizes the neuron after a burst. Each neuron, which is a conditional oscillator, is coupled to all other RE neurons via fast gamma-aminobutyric acid-A (GABAA) and slow GABAB synapses. 3. For generating network oscillations IAHP may not be necessary. Synaptic inhibition can provide the hyperpolarization for deinactivating ICa-T that causes bursting if the reversal potentials for GABAA and GABAB synapses are sufficiently negative. 4. If model neurons display sufficiently powerful rebound excitability, an isolated RE network of such neurons oscillates with partial but typically not full synchrony. The neurons spontaneously segregate themselves into several macroscopic clusters. The neurons within a cluster follow the same time course, but the clusters oscillate differently from one another. In addition to activity patterns in which clusters burst sequentially (e.g., 2 or 3 clusters bursting alternately), a two-cluster state may occur with one cluster active and one quiescent. Because the neurons are all-to-all coupled, the cluster states do not have any spatial structure. 5. We have explored the sensitivity of such partially synchronized patterns to heterogeneity in cells' intrinsic properties and to simulated neuroelectric noise. Although either precludes precise clustering, modest levels of heterogeneity or noise lead to approximate clustering of active cells. The population-averaged voltage may oscillate almost regularly but individual cells burst at nearly every second cycle or less frequently. The active-quiescent state is not robust at all to heterogeneity or noise. Total asynchrony is observed when heterogeneity or noise is too large, e.g., even at 25% heterogeneity for our reference set of parameter values. 6. The fast GABAA inhibition (with a reversal potential more negative than, say, -65 mV) favors the cluster states and prevents full synchrony. Our simulation results suggest two mechanisms that can fully synchronize the isolated RE network model. With GABAA removed or almost totally blocked, GABAB inhibition (because it is slow) can lead to full synchrony, which is partially robust to heterogeneity and noise.(ABSTRACT TRUNCATED AT 400 WORDS)

Corrigenda for Synchronization properties of spindle oscillations in a thalamic reticular nucleus model

Pages 1109–1126: D. Golomb, X.-J. Wang, and J. Rinzel, “Synchronization properties of spindle oscillations in a thalamic reticular nucleus model.” The following errors were inadvertently introduced when this article was printed. Page 1125, in the list of references, all the journal titles written as Physiol. Rev. should be Phys. Rev., and all the journal titles written as Physiol. Rev. Lett. should be Phys. Rev. Lett.